Exp Brain Res (2005) 160: 245–258 DOI 10.1007/s00221-004-2010-2
RESEARCH ARTICLES
John F. Soechting . Leigh A. Mrotek . Martha Flanders
Smooth pursuit tracking of an abrupt change in target direction: vector superposition of discrete responses
Received: 30 March 2004 / Accepted: 10 June 2004 / Published online: 18 August 2004 # Springer-Verlag 2004
Abstract The directional control of smooth pursuit eye movements was studied by presenting human subjects with targets that moved in a straight line at a constant speed and then changed direction abruptly and unpredictably. To minimize the probability of saccadic responses in the interval following the target’s change in direction, target position was offset so as to eliminate position error after the reaction time. Smooth pursuit speed declined at a latency of 90 ms, whereas the direction of smooth pursuit began to change later (130 ms). The amplitude of the offset in target position did not affect the subsequent smooth pursuit response. In other experiments, the target’s speed or acceleration was changed abruptly at the time of the change in direction. Step changes in speed elicited short-latency responses in smooth pursuit tracking but step changes in acceleration did not. In all instances, the earliest component of the response did not depend on the parameters of the stimulus. The data were fit with a model in which smooth pursuit resulted from the vector addition of two components, one representing a response to the arrest of the initial target motion and the other the response to the onset of target motion in the new direction. This model gave an excellent fit but further analysis revealed nonlinear interactions between the two vector components. These interactions represented directional anisotropies both in terms of the initial tracking direction (which was either vertical or 45°) and in terms of the cardinal directions (vertical and horizontal). Keywords Eye movements . Human subjects . Target acceleration . Target velocity
J. F. Soechting (*) . L. A. Mrotek . M. Flanders Department of Neuroscience, University of Minnesota, 6-145 Jackson Hall, 321 Church St. SE, Minneapolis, MN 55455, USA e-mail:
[email protected] Tel.: +1-612-6257961 Fax: +1-612-6265009
Introduction During smooth pursuit, eye velocity is controlled so as to match the target’s velocity (Keller and Heinen 1991; Lisberger et al. 1987; Rashbass 1961). Thus, the control signal is primarily related to the target’s velocity, although signals related to target position and acceleration contribute to a lesser extent (Krauzlis and Lisberger 1994b; Pola and Wyatt 1980). Velocity is a vector quantity with a direction and magnitude and to date, most of the work has concerned how the magnitude of the velocity of the eye is related to that of the target. Less attention has been devoted to the directional control of smooth pursuit eye movements (Leung and Kettner 1997; Leung et al. 2000). If there is an uncertainty about the target’s direction (as provided by two stimuli moving in different directions), the initial response of smooth pursuit reflects a vector average of the response to the individual target motions (Ferrera 2000; Gardner and Lisberger 2001, 2002; Lisberger and Ferrera 1997). Similarly, when a multifaceted object is tracked, the initial response reflects a vector average of the component motions, i.e., the motions of each side, rather than the actual motion of the target (Masson and Stone 2002). These observations suggest that a model of smooth pursuit that treats the inputs and outputs as vectors (such as position, velocity and acceleration), rather than as scalars, would be an appropriate generalization. However, the results of a recent study of manual tracking suggest a different parameterization (Engel and Soechting 2000). We used a task in which the target initially moved at a constant speed and then unpredictably changed direction. We described the response in terms of the speed and direction of the finger motion, i.e., by two scalar quantities. After the target changed direction, hand speed initially declined, and this deceleration was graded with the amount by which the target changed direction. The direction of hand motion changed gradually and monotonically. The latency for the change in speed was less than the latency for the change in direction, suggesting that these parameters were controlled separately. In fact, a
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control model based on this assumption provided an excellent fit to the data. We also studied ocular tracking of the same set of stimuli and found that the time course of smooth pursuit exhibited remarkable similarities to that of manual tracking (Engel and Soechting 2003; Engel et al. 1999, 2000). Specifically, as was the case for manual tracking, smooth pursuit declined in speed before it changed direction (Engel et al. 2000). However, since smooth pursuit was generally interrupted by a saccade to the target, we did not attempt to model these responses quantitatively. In the present study, we reexamined this issue by introducing a modification to the target motion (following Rashbass 1961) which decreases the probability of saccades around the time of the change in target direction. Thus, in the present experiments, the target underwent a step change in position coincident with the change in direction. In agreement with our previous results, the latency for the change in smooth pursuit speed was less than the latency for the change in direction. However, in contrast to the results obtained for manual tracking, the initial deceleration in the direction of target motion did not depend on the amount by which the target changed direction. Accordingly, the experimental data could be explained by a model based on the vector superposition of a stereotypical response to the arrest of the initial target motion followed by a directional response to the onset of the new target motion. Although this simple two-component model fit the data well, an even better fit was obtained by including direction-dependent anisotropies in the gain of the response.
Fig. 1 Response to a step change in the direction of target motion. The left panel shows the motion of the target (heavy trace), which was initially downward and then changed abruptly by 150° upward and to the right. At the time that the direction changed, the target was also displaced so that the target’s motion would ideally intercept the gaze trajectory. The lighter trace shows the gaze trajectory;
Methods Subjects Twelve subjects (seven males and five females) participated in these experiments. Their vision was normal or corrected to normal. All gave their informed consent to procedures that were reviewed and approved by the Institutional Review Board of the University of Minnesota. Experimental overview Experimental procedures and methods for data acquisition and analysis were similar to those described previously (Engel and Soechting 2003; Mrotek et al. 2004). Subjects tracked targets presented on a computer monitor (Mitsubishi Diamond Scan 20 M) with a resolution of 640×480 pixels (34.8×26.0 cm) and a 60-Hz refresh rate. They sat about 60 cm from the screen, placed at eye level in a dimly lit room. Eye movements were recorded binocularly at a sampling rate of 250 Hz with headmounted infrared cameras (SMI Eye Link). In most experiments, the target initially appeared at the top center of the screen and began moving downward (positive y-direction) at a speed of 240 pixels/s (12.6°/s). The target was a cyan circle, with a radius of 4 pixels (0.2° of visual angle). After the target had traveled between 5/12 and 2/3 of the distance to the bottom of the screen, it underwent a sudden change in direction. Thus, direction changed at a random time in a 1/2-s interval. The amount by which direction changed was also randomized and ranged from 0 to ±150° in 30° increments. At the start of each trial, a red fixation spot directed gaze to a point 2.1° below the top of the screen.
thicker dotted lines indicate saccades. The panels on the right show target and gaze direction (upper panel) and speed (lower panel) for the same trial. The vertical line denotes the time when the target changed direction. The change in direction resulted in a transient decrease in the speed of smooth pursuit and a gradual change in its direction
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Simultaneously with the change in direction, the target underwent a step change in position (see Fig. 1). The amplitude and the direction of the step were designed so that eye position and target position would coincide at the end of the smooth pursuit reaction time (120 ms, see de Brouwer et al. 2002b). Accordingly, the vertical position of the new target trajectory was displaced downward (d1in Fig. 1) by the amount the eye would travel in 120 ms, assuming perfect tracking. Since pursuit speed initially decreases (Engel et al. 1999), we introduced an additional delay of 30 ms so that the target would intercept the y-axis 150 ms after the change in direction. Thus the target’s new direction began with the offset labeled d2 in Fig. 1. We took care not to artificially introduce a discontinuity in speed. Let frame 0 correspond to the time at which direction changes. On the preceding frame (−1), we presented two targets: the first displaced according to the initial downward motion and the second appearing at the new position. On the subsequent frame (0), the first target disappeared and the second target was displaced in the new direction. Thus, in each frame, only one target was in motion: the first target in frame (−1) and the second target
Fig. 2a, b Effect of varying the amplitude of the step change in target position. The target motions are indicated in the left panels (for a 60° change in direction in a and a 120° change in direction in b). The three line styles (solid, dotted and dashed) denote three different amplitudes of step change in target displacement. The right panels show averaged records of speed and direction for one subject in the three experimental conditions. The bottom panel shows the probability of the occurrence of a saccade at various times, using data for all subjects in Exps. 1 and 2 (largest step displacement). Note that this probability was low prior to the change in the direction of target motion, decreased almost to zero shortly after direction changed at time 0, and subsequently rose to a peak at about 300 ms
in frame (0). Accordingly, the target’s speed was not influenced by the amplitude of the step displacement. Experimental design We studied four different experimental conditions, with four subjects participating in each experiment. One subject took part in three experiments, and two others took part in two experiments. Experiment 1: effect of a step change in target direction This experiment implemented the basic design described in the overview and examined the effect of the initial direction of target motion on the response. In one block of trials, the target initially traveled downward at 12.6°/s, and then underwent a step change in position and direction. In a second block of trials, the target initially traveled downward and to the right (45°) at the same speed. In each block, there were 11 directions of subsequent target
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motion, equally spaced in 30° increments and 12 repeats per condition. The new direction and the time at which it began were randomized from trial to trial. Experiment 2: effect of the size of step displacement In this experiment, we varied the size of the step displacement of the target by three different amounts: the nominal one used in Exp. 1, and ones that were 2/3 or 1/3 as large (see left panels of Fig. 2). In each instance, target speed was constant throughout the trial. There were seven trials for each experimental condition (direction and amount of offset), for a total of 231 trials (11 directions × 3 conditions × 7 repeats). Target direction, offset and the time of the change in target direction were randomized. Experiment 3: effect of a step change in target speed In this experiment, the target could undergo a step change in speed by ±50% at the time of the change in the target’s direction. On one third of the trials, target speed did not change from its original value of 12.6°/s. The offset in the step change in target position (d1and d2) was adjusted for each speed to minimize tracking error. There were 11 directions × 3 speeds × 8 repeats for a total of 264 trials. Experiment 4: effect of a step change in target acceleration Immediately following the change in the direction of target motion, the target could accelerate or decelerate at a constant rate. Target acceleration (12.6°/s2) was maintained for 0.5 s, such that target speed had changed by ±50% at the end of 0.5 s. Target acceleration was zero in one third of the trials. Since speed changed gradually, we did not vary the amount by which target position was offset. Data analysis Sampled data were calibrated using a procedure performed at the onset of each session, with drift compensation performed prior to each trial. The x- and y-position data were filtered (double-sided exponential filter with 4 ms time constant) and numerically differentiated. Saccades were removed by interpolating the velocity traces with a cubic spline and the desaccaded data were averaged, after aligning each trial on the time at which target motion changed (for additional details see Engel and Soechting 2003; Mrotek et al. 2004). The speed (s) and direction (θ) of smooth pursuit were computed from the x- and ycomponents of velocity:
1=2 s ¼ v2x þ v2y
¼ tan1 vx =vy
(1)
The appropriate models were then fit to average speed, direction or velocity, in order to quantify the influence of the experimental variables.
Results Smooth pursuit response to a step change in target direction After the direction of target motion changed, the speed of smooth pursuit decreased transiently and its direction changed smoothly and gradually, in agreement with previous observations (Engel and Soechting 2003; Engel et al. 2000). This is evident in the results from the single trial illustrated in Fig. 1. The target initially traveled downward, and then underwent a step change in position, changing its course to move 150° upward and to the right from the vertical (left panel). The offset in the target position was chosen so that, at the time when smooth pursuit began to respond to the change in target motion, gaze position (indicated by the light trace in the left panel) would coincide with the position of the target. This experimental design minimized the probability of saccades interrupting smooth pursuit, particularly around the time at which the target changed direction. In this example, there was one saccade (indicated by heavier, dashed lines) early in the trial (around 0.4 s), and a second one about 600 ms after the target had changed direction. Smooth pursuit speed (shown in the lower right panel of Fig. 1) on average was slightly less than target speed prior to the change in target direction (vertical line at 1.2 s). Over all trials, the average gain for this subject was 0.90, evaluated in the 100-ms interval prior to the target’s change in direction. Average gain for all subjects in Exps. 1 and 2 was 0.73 in this interval. Shortly after the change in target direction, speed decreased transiently and then reacquired the target’s speed. Pursuit gain after direction had changed was slightly larger (0.98 evaluated in the interval between 400 and 500 ms), a result that was typical (average 0.93 for Exps. 1 and 2). The latency for the change in the direction (top right panel) appeared to be somewhat greater than the latency for the decrease in speed. The results illustrated in Fig. 1 were typical of the results obtained in this experimental condition, as can be ascertained from the averaged data shown in Fig. 2 for two other target directions (60° in Fig. 2a and 120° in Fig. 2b). In each panel, three traces are superposed, corresponding to the different amounts of target displacement (Exp. 2). The solid traces correspond to the nominal values of target displacement (the amount designed to minimize tracking error), while the dotted and dashed traces correspond to step displacements that were 1/3 and 2/3 less. In Fig. 2, the latency for the change in tracking speed is about 80 ms, and the latency for the change in direction is much longer
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(~130 ms). Furthermore, the amount of the target displacement did not influence the speed or the direction of smooth pursuit in any consistent or significant way. Statistical analysis supported this conclusion. For speed, we computed the time and the amplitude of the minimum in speed. Both parameters depended on the amount by which target direction changed, but they did not depend on the size of the step displacement (ANOVA, F(2,99)=0.885 for amplitude, F(2,99)=0.245 for time, p>0.05). The latency for the decline in speed (estimated by regression analysis of the initial transient) averaged 90±2 ms (SE), and did not depend on the target direction or on the size of the step displacement (F(2,99)=1.183, p>0.05). To characterize the time course of the change in smooth pursuit direction, we fitted the averaged data for each experimental condition with the logistic distribution function: ðtÞ ¼ f = 1 þ eðt Þ= (2)
100 ms, as shown in the plot of saccade direction in Fig. 3b. In this plot, the sign of the saccade direction (relative to initial target direction) is defined by the new direction of target motion, a negative angle corresponding to saccades that were in the direction of the step in target position (as in Fig. 3a). Statistically, for saccades starting before +56 ms (relative to the time at which target direction changed), saccade direction did not differ from 0 (t-test, Bonferroni correction for multiple comparisons, p>0.05). Thereafter, until +88 ms, saccade direction was consistently negative (−14.8°, p0.05, F(2,78)=0.770 for latency and F(2,78)=0.759 for rise time).
As demonstrated above, the experimental design eliminated most saccades just after the change in direction and allowed us to examine smooth pursuit. Although the main goal was to describe the influence of specific target parameters, it is known that expectations about target motion can influence smooth pursuit (Kowler 1989; Kowler et al. 1984). In our experimental design, the ultimate direction of target motion was unpredictable, as was the time at which the target changed direction. Nevertheless, it is possible that the stimulus and the tracking behavior on one trial influenced the response on the subsequent trial (cf. Thoroughman and Shadmehr 2000). We assessed this possibility by using the following model:
Saccades The bottom trace in Fig. 2 shows that the experimental design succeeded in reducing the probability of saccades around the time that the target changed direction. Prior to this time, there was an 8% probability of a saccade at any instant. At about 100 ms after the target step, this probability decreased dramatically and then increased, reaching a peak of 45% at 300 ms. (Note that by 300 ms, the direction of smooth pursuit had matched the new target direction and its speed had recovered from the transient decrease.) These results correspond to the instances in which the step displacement was designed to minimize the probability of saccades. Saccade probability increased and its latency decreased for smaller step displacements. When the step displacement was 2/3 of the optimal amount, the probability reached a maximum of 65% at 260 ms; when it was 1/3 of the optimal amount, the corresponding values were 75% at 236 ms. In the few instances in which saccades were initiated in the interval 50–100 ms after the change in target direction, the saccade direction tended to reflect the step change in the target’s position. An example is provided in Fig. 3a. In this example, the saccade initiated 68 ms after the target had changed direction was directed −27° from the vertical (down and to the left), compensating for the jump in the target’s position. This behavior was characteristic of saccades that occurred in the interval between 50 and
Influence of previous trial
Fig. 3a, b Saccade direction related to target position. a Tracking of a target whose motion changed by 60° to the right. Smooth pursuit is indicated by light, solid lines and saccades are denoted by heavier, dashed lines. Note that the saccade initiated shortly (68 ms) after the change in the target’s direction is directed 27° to the left, toward the target that was displaced to the left. b Saccade direction for all instances in which a saccade began in the interval −50 to +100 ms relative to the time at which target direction changed. Positive saccade directions are in the direction of the new target velocity, whereas negative saccade directions are in the direction of the target’s position immediately after the change in direction
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sji ðtÞ ¼ ji ðtÞ ¼
As ðtÞsil ðtÞ þ Bs ðtÞsj ðtÞ A ðtÞil ðtÞ þ B ðtÞj ðtÞ
(3)
where s and θ refer to speed and direction, the subscript i refers to the ith trial and the superscript j refers to the jth experimental condition (i.e., direction and step size in Exp. 2). s j and j denote the averages of speed and direction for all trials for that particular condition. The weighting coefficients A and B were obtained from a leastsquares fit of all of the data for each session. To decrease the amount of variability in the data, we assumed that these coefficients were constant over 40-ms intervals, and computed them every 20 ms (i.e., we used a moving average). The outcome of this analysis is shown in Fig. 4, which depicts results from all 16 sessions in which the target initially moved downward. If the previous trial had no influence on the response, then the weighting coefficient for the average (Fig. 4b) should be 1.0, and that for the previous trial (Fig. 4a) should be 0.0. This was true beginning about 300 ms after the target had changed direction. However the response on the preceding trial did initially influence the speed and the direction of smooth pursuit on the present trial, with a positive weighting coefficient. Statistically, the weighting coefficient of the previous trial for speed (As) differed from 0 in the interval from 0 to 220 ms (mean weight = 0.073, p
